A362341 -id:A362341 - cp's OEIS frontend

A362340 a(n) = n! * Sum_{k=0..floor(n/2)} (-k/2)^k / (k! * (n-2*k)!).

1, 1, 0, -2, 7, 51, -239, -2435, 16353, 209377, -1826099, -28232379, 303020125, 5494172893, -70032035163, -1457369472299, 21512472563281, 505400696581905, -8478758871011807, -221971772323923263, 4171251104170567101, 120416449897739144941

Offset: 0

Seiichi Manyama, Apr 17 2023

sign

Eric Weisstein's World of Mathematics, Lambert W-Function.

Cf. A069856, A362341, A362342.

Cf. A362276.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(x^2/2))))

E.g.f.: exp(x) / (1 + LambertW(x^2/2)).

A362342 a(n) = n! * Sum_{k=0..floor(n/4)} (-k/24)^k / (k! * (n-4*k)!).

Original entry on oeis.org

1, 1, 1, 1, 0, -4, -14, -34, 71, 1135, 6091, 22771, -87119, -1847559, -13769755, -70046339, 390688481, 10473961121, 100030347361, 643972996705, -4717305354419, -153449916040259, -1787926183752939, -13926752488607419, 126329848106764765

Offset: 0

Seiichi Manyama, Apr 17 2023

sign

Eric Weisstein's World of Mathematics, Lambert W-Function.

Cf. A069856, A362340, A362341.

Cf. A351930, A362345, A362349.

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(x^4/24))))

E.g.f.: exp(x) / (1 + LambertW(x^4/24)).

cp's OEIS Frontend

A362340 a(n) = n! * Sum_{k=0..floor(n/2)} (-k/2)^k / (k! * (n-2*k)!).

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